Title
Flowhop Scheduling mit parallelen Genetischen Algorithmen: Eine problemorientierte Analyse genetischer Suchstrategien (German Ed,Used
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rungs problem en in unterschiedlichen wissenschaftlichen Disziplinen anwen deten [Gold89. 1, S. 126130]. Das Optimierungsproblem in seiner allgemeinsten Form ist die Aufgabe Optimiere + f (x), XEM, (10) n n mit f als reellwertiger Funktion des lR und M C lR als Raum aller zulassigen Lasungen. Die Optimierung beliebiger reeller Funktionen unter Verwendung Genetischer Algorithmen wurde zuerst in der Dissertation von de Jong [Jong75] behandelt. Die von ihm experimentell untersuchten unste tigen, nichtkonvexen, multimodalen und stochastischen Funktionen dienen in der Literatur seither als Standardprobleme zur Validierung genetischer Optimierungsstrategien, siehe etwa [MSB91]. Wird in der Formulierung der Aufgabe (10) zusatzlich die Ganzzahligkeitsbedingung an die Kompo nenten der Lasungsvektoren x gekntipft, so fallt das Problem bekanntlich in den Bereich der kombinatorischen Optimierung. An einem einfachen Beispiel soll das konstruktive Paradigma der genetischen Optimierung ein gefiihrt werden. Hierzu werden wir eine der Biologie entlehnte begrifHiche Analogie verwenden, die in Abschnitt 3. 2 zusammenhangend dargestellt wird. Es sei die Aufgabe 2 Max + f(x, y)=x 2xy+y2, O::: x, y::: klmitx, yElN (11) 2 mit k als Zweierpotenz, also z. B. k = 32, gegeben. Jedes der 32 unter schiedlichen 2Tupel, welche als potentielle Optimallasungen der Aufgabe zur Diskussion stehen, bezeichnet den Phanotyp einer zulassigen Lasung. Dieser laBt sich tiber eine Binartransformation in zwei Strings der Lange log2 k darstellen. x) = ( 25 ) 11 1 0 0 1 I (12) ( y 14 + 0 1 1 1 0 Die geordnete Menge binarer Strings definiert den Genotypus einer Lasung.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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